The algebra of first-order symmetry operators of the Dirac equation on four-dimensional Lie groups with right-invariant metric is investigated. It is shown that the algebra of symmetry operators is in general not a Lie algebra. Noncommutative reduction mediated by spin symmetry operators is investigated. For the Dirac equation on the Lie group SO(2,1) a parametric family of particular solutions obtained by the method of noncommutative integration over a subalgebra containing a spin symmetry operator is constructed.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 25–32, August, 2016.
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Breev, A.I., Mosman, E.A. Noncommutative Integration and Symmetry Algebra of the Dirac Equation on the Lie Groups. Russ Phys J 59, 1153–1163 (2016). https://doi.org/10.1007/s11182-016-0885-6
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DOI: https://doi.org/10.1007/s11182-016-0885-6